FIG. 1 illustrates a conventional boiler water reactor. As shown, a jet pump 110 supplies water to a reactor vessel 112 housed within a containment vessel 114. The core 116 of the reactor vessel 112 includes a number of fuel bundles such as described in detail below with respect to FIG. 2. The controlled nuclear fission taking place at the fuel bundles in the core 116 generates heat which turns the supplied water to steam. This steam is supplied from the reactor vessel to turbines 118, which power a generator 120. The generator 120 then outputs electrical energy. The steam supplied to the turbines 118 is recycled by condensing the steam back into water at a condenser 122, and supplying the condensed steam back to the jet pump 110.
FIG. 2 illustrates a fuel bundle in the core 116 of the reactor vessel 112. A typical core will contain anywhere from 200 to 900 of these bundles B. As shown in FIG. 2, the bundle B includes an outer channel C surrounding a plurality of fuel rods 100 extending generally parallel to one another between upper and lower tie plates U and L, respectively, and in a generally rectilinear matrix of fuel rods as illustrated in FIG. 3. The rods 100 are maintained laterally spaced from one another by a plurality of spacers S vertically spaced from the other along the length of the fuel rods within the channel C. Referring to FIG. 3, there is illustrated in an array of fuel rods 100, i.e., in this instance, a 10×10 array, surrounded by the fuel channel C. The fuel rods 100 are arranged in orthogonally related rows and also surround one or more water rods, two water rods 130 being illustrated. The fuel bundle B is arranged in one quadrant of a control rod 132 as is conventional. It will be appreciated that a fuel bundle is typically arranged in each of the other quadrants of the control rod 132. Movement of the control rod 132 up between the bundles B controls the amount of reactivity occurring in the bundles B in association with that control rod 132.
A boiling water reactor such as illustrated in FIG. 1 operates for a cycle of typically one, one and a half or two years. Specifically, a core of the reactor is designed to generate a certain amount of energy measured in gigawatt days per metric ton of uranium (GWD/MTU) over a cycle before being replaced with a new core. Core design typically involves a constraint optimization problem wherein a best possible solution that maximizes energy output is developed according to various well-known algorithms.
Namely, the solution to such a problem typically involves a mathematical search algorithm, whereby successively improved solutions are obtained over the course of a number of algorithm iterations. Each iteration, which can be thought of as a proposed solution, results in improvement of an objective function. An objective function is a mathematical expression having parameter values of a proposed solution as inputs. Typically, the objective function includes one or more mathematical expressions representing constraints of the problem at issue and the parameter or parameters being maximized/minimized. The objective function produces a figure of merit for the proposed solution. Comparison of objective function values provides a measure as to the relative strength of one solution versus another. Numerous search algorithms exist and differ in, for example, (1) the manner by which the control variables for a particular problem are modified, (2) whether a population of solutions or a single solution is tracked during the improvement process, and (3) the method for assessment of convergence. However, these search algorithms rely on the results of an objective function in deciding a path of convergence.
At the beginning of cycle (BOC), the core design is put into operation. As is also typical, actual reactor performance often deviates from the performance modeled in generating the core design. Accordingly, adjustments from the operational model are quite often made in order to maintain performance of the reactor before the end of cycle (EOC).
Some of the issues that arise during plant operation, which require such adjustments, can be classified according to the following:
1) mechanical degradation of the fuel or system components, that may require specific changes in reactor operation as well as imposition of additional constraints; and
2) deviations in predicted versus anticipated measured plant parameters of sufficient magnitude to require additional conservatism in reactor operation.
Among category 1), the following are exemplary events that have occurred in recent years:
1a) Leaking Fuel Rod
In this scenario, off-gas is detected indicating a ruptured fuel rod. Control blades are inserted in the area surrounding the suspect fuel rod in the hopes of reducing the off-gas, because in this case, off-gas release is a function of local power within the fuel rod. Normal operational practice is to fully insert control blades in the immediate location of the leaking fuel rod as well as possible locations immediately surrounding the fuel rod. The consequence of such action is suppression of power for the remainder of the cycle with an accompanying penalty (loss) of cycle energy.
1b) Fuel Batch Corrosion
Following a fuel inspection, a particular batch of once-burned, highly reactive fuel indicates accelerated corrosion spread across a large number of bundles within the grouping. Current practice would be to extend the outage, replacing the problem fuel bundles with fuel from the spent fuel pool or with fresh fuel. Alternatively, one could simply shuffle the problem bundles into ‘benign’ core locations of lower power, such as core periphery. In either scenario, a new loading pattern would need to be generated and licensed, which can be costly as well as delay plant startup. In the former case, use of fresh bundles would incur additional cost while in the latter case, shuffling to the periphery would result in a substantial loss of energy.
1c) Flow Degradation Due to Jet Pump Failure
In this scenario, the reactor flow capability (i.e. the ability to maintain the rated flow) is projected to degrade with time due to the accumulation of crud deposits in the jet pump drive flow nozzles. Since ‘cleaning’ the jet pumps to remove such crud is a costly endeavor (about 4 million dollars per cycle), utilities may choose to allow some flow degradation if the fuel cycle economic penalty is not too high. The rate of flow degradation, based on historical data, is estimated to be a certain rate. However, it is also known that the uncertainty with this estimate is fairly high.
1d) Degradation of Steam Separators
In this scenario, an increase in steam production in certain ‘hot’ areas of the reactor core result in a decrease in the steam separation efficiency (i.e., the ability to remove water liquid from the steam/water mixture). As a result, a greater amount of liquid is carried through the separators, through the steam lines, and on to the turbine blades (liquid impinging on turbine blades can erode the blades). This scenario is most likely during a power uprate (since the separators were ‘sized’ for a particular steam/liquid flow rate). A solution is to replace the separators with ‘improved’ versions that are more efficient at handling the higher steam qualities.
Under category 2) the following are a couple exemplary scenarios:
2a) Thermal Limit
Historical operating data indicates that the reactor measured local power is greater than the predicted local power during a certain time period of the operating cycle. Because of this deviation, the plant is in jeopardy of violating the constraint on thermal limit. A thermal limit is any one of several design constraints related to nuclear heat generation and dissipation that protect the integrity of the nuclear fuel rod. In order to satisfy regulatory requirements, the plant would be forced to reduce overall power level until the measured local power violation of the constraint limit was eliminated. This reduced power level would have to be maintained until sufficient margin was made available, either through fuel depletion or through control blade and flow maneuvers, in order to return the plant to full power operation. A power reduction of this nature, if only a few percent, has tremendous negative economic impact to the plant.
2b) Operation Beyond Historical Operational Experience
Extending cycle length beyond that normally anticipated puts the reactor in an operational realm where biases between predicted and measured data are not well established. In addition, no measurements will become available during the operating cycle until just before shutdown, at which point measurements will be performed. An example is the cold shutdown margin, which is a measure of how far away the reactor is from achieving a self-sustaining nuclear chain reaction during a shutdown condition with control rods fully inserted. In this situation, there is a need to apply additional conservatisms on the constraint limit values during the design phase. This additional conservatism can result in a less efficient fuel cycle design.